Exam 12: Analysis of Variance

A study was recently conducted to see whether the mean starting salaries for graduates of engineering, business, healthcare, and computer information systems majors differ. A random sample of 8 graduates was selected from each major. The following chart shows some of the results of the ANOVA computations; however, some of the output is missing. If it had been included, the calculated test statistic would be F = 8.33.

A start-up cell phone applications company is interested in determining whether house-hold incomes are different for subscribers to three different service providers. A random sample of 25 subscribers to each of the three service providers was taken, and the annual household income for each subscriber was recorded. The partially completed ANOVA table for the analysis is shown here: Based on the sample results, can the start-up firm conclude that there is a difference in household incomes for subscribers to the three service providers? You may assume normal distributions and equal variances. Conduct your test at the alpha= 0.10 level of significance. Be sure to state a critical F-statistic, a decision rule, and a conclusion.

In a two-factor ANOVA design with replication, the null hypothesis for testing whether interaction exists is that no interaction exists. The alternative hypothesis is that interaction does exist.

In conjunction with the housing foreclosure crisis of 2009, many economists expressed increasing concern about the level of credit card debt and efforts of banks to raise interest rates on these cards. The banks claimed the increases were justified. A Senate subcommittee decided to determine if the average credit card balance depends on the type of credit card used. Under consideration are Visa, MasterCard, Discover, and American Express. The sample sizes to be used for each level are 25, 25, 26, and 23, respectively. State the number of degrees of freedom available for determining the within-samples variation.

In a randomized complete block design analysis of variance, how many factors are there to be analyzed?

A test is conducted to compare three different income tax software packages to determine whether there is any difference in the average time it takes to prepare income tax returns using the three different software packages. Ten different persons' income tax returns are done by each of the three software packages and the time is recorded for each. The computer results are shown below. Assuming that the hypothesis tests are conducted using a significance level equal to 0.05, the Fisher's LSD value for multiple comparisons is:

Suppose that you have just performed an experiment using the randomized complete block analysis of variance design and the output from Excel is shown as follows. The primary null hypothesis to be tested involves whether the means of the three groups are equal. ANOVA: Two-Factor Without Replication Using a significance level of 0.05, what conclusions should be made about the three groups? Which groups have different means? Discuss.

In conjunction with the housing foreclosure crisis of 2009, many economists expressed increasing concern about the level of credit card debt and efforts of banks to raise interest rates on these cards. The banks claimed the increases were justified. A Senate subcommittee decided to determine if the average credit card balance depends on the type of credit card used. Under consideration are Visa, MasterCard, Discover, and American Express. The sample sizes to be used for each level are 25, 25, 26, and 23, respectively. State the number of degrees of freedom available for determining the between-samples variation.

A company's customer service department wants to compare the average service times at three different service locations. It wants to conduct a hypothesis test to determine if all three means are the same or not, at the 0.05 level of significance. If n =10 observations are taken at each of the three restaurants, the critical value is F = 3.354.

Considering the following printout for a two-factor ANOVA design, which of the following is a proper conclusion to reach?

An Internet service provider is interested in testing to see if there is a difference in the mean weekly connect time for users who come into the service through a dial-up line, DSL, or cable Internet. To test this, the ISP has selected random samples from each category of user and recorded the connect time during a week period. The following data were collected: Based upon these data and a significance level of 0.05, which of the following statements is true?

An Internet service provider is interested in testing to see if there is a difference in the mean weekly connect time for users who come into the service through a dial-up line, DSL, or cable Internet. To test this, the ISP has selected random samples from each category of user and recorded the connect time during a week period. The following data were collected: Assuming that the test is to be conducted at a 0.01 level of significance, what would the critical value be for this test?

Examine the following two-factor analysis of variance table: Determine if interaction exists between factor A and factor B. Use alpha = 0.05.

The Tukey-Kramer method for multiple comparisons can only be used when the analysis of variance design is balanced.

In a two-factor ANOVA design, the variances of the populations are assumed to be equal unless there is interaction present.

Three brands of running shoes are each tested by 10 different runners. The amount of wear on the sole of the shoes is then measured. The objective is to determine if there is any difference among the three brands of shoes based on how long the soles last. This means that there is one factor with 10 levels and 3 blocks.

The Lottaburger restaurant chain in central New Mexico is conducting an analysis of its restaurants, which take pride in serving burgers and fries to go faster than the competition. As a part of its analysis, Lottaburger wants to determine if its speed of service is different across its four outlets. Orders at Lottaburger restaurants are tracked electronically, and the chain is able to determine the speed with which every order is filled. The chain decided to randomly sample 20 orders from each of the four restaurants it operates. The speed of service for each randomly sampled order was noted and is contained in the file Lottaburger. At the alpha = 0.05 level of service, can Lottaburger conclude that the speed of service is different across the four restaurants in the chain?

A national car rental agency is interested in determining whether the mean days that customers rent cars is the same between three of its major cities. The following data reflect the number of days people rented a car for a sample of people in each of three cities. Assuming that a one-way analysis of variance is to be performed, the value of the test statistic is approximately F = 3.4.

The general idea is that interaction between two factors means that the effect due to one of the factors is not uniform across all levels of the other factor.

Which of the following describes a treatment in a randomized complete block analysis of variance?